How do you integrate 3ye^3z dz using u substitution?

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Homework Help Overview

The discussion revolves around the integration of the expression 3ye3z dz, specifically focusing on the application of u-substitution in the integration process.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of u-substitution, with one suggesting u=3z and du=3dz. Questions arise regarding the correctness of the resulting expression after integration and whether it aligns with the original function when differentiated.

Discussion Status

The conversation includes attempts to clarify the integration process and verify the results through differentiation. Some participants provide feedback on the correctness of the expressions derived from the integration attempt, indicating a collaborative effort to refine understanding.

Contextual Notes

There is an indication of confusion regarding the integration steps and the relationship between differentiation and integration in this context. Participants are checking assumptions about the integration method and the resulting expressions.

stevecallaway
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Homework Statement



Needing to integrate 3ye^3z dz

Homework Equations





The Attempt at a Solution


I believe you use u substitution and u=3z du=3dz
Then you get yze^3z. Is this correct?
 
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If you differentiate yze3z with respect to z do you get what you started with? I don't think so, but can you fix it?
 
>>Then you get yze^3z. Is this correct?
No completely, you have an extra factor of z
 
I believe differentiating ye^3z with respect to z will give 3ye^3z. Therefore, integrating 3ye^3z dz will be ye^3z. Correct?
 
Yes.
 
Sweet,thanks to the both of you
 

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